Biological imaging by soft x-ray diffraction microscopy

Abstract

We have used the method of x-ray diffraction microscopy to image the complex-valued exit wave of an intact and unstained yeast cell. The images of the freeze-dried cell, obtained by using 750-eV x-rays from different angular orientations, portray several of the cell's major internal components to 30-nm resolution. The good agreement among the independently recovered structures demonstrates the accuracy of the imaging technique. To obtain the best possible reconstructions, we have implemented procedures for handling noisy and incomplete diffraction data, and we propose a method for determining the reconstructed resolution. This work represents a previously uncharacterized application of x-ray diffraction microscopy to a specimen of this complexity and provides confidence in the feasibility of the ultimate goal of imaging biological specimens at 10-nm resolution in three dimensions.

Fig. 1.

Soft x-ray diffraction pattern of a freeze-dried yeast cell. (Left) The assembled pattern shown represents the summation of several diffraction patterns, with a total exposure of 65 seconds to 750-eV x-rays. The assembled pattern covers 1200 × 1200 pixels of the 1340 × 1300 original array and extends to a spatial frequency, or diffraction angle divided by wavelength, of 48 inverse micrometers at the edges and 68 inverse micrometers at the corners. A spatial frequency of 48 inverse micrometers at the edges corresponds to a half-period pixel size in real space of 10 nm. The speckles in the diffraction pattern have a consistent size associated with the inverse of the size of the yeast cell. (Right) Power spectrum as a function of spatial frequency.

Fig. 2.

Technical details of the reconstruction of the diffraction data of Fig. 1. (Left) Because the very intense nondiffracted beam was blocked by a beamstop, no data were recorded at very low spatial frequencies. Shown here are two modes in the reconstruction superimposed on the missing data region of the detector (white pixels in the diffraction or Fourier space in B and D). We also show these modes in object space, superimposed on the support (allowed spatial region) of the yeast cell (A and C). The amplitudes of weakly constrained modes such as these are undetermined by our reconstruction. (Right) One measure of the quality of the reconstruction is the degree to which it reproduces the recorded data (diffraction intensities). The reconstructions of Fig. 3 are averages I_recon = | 〈F_recon 〉 | of many complex iterates F_recon of a phasing algorithm, each differing only in the values of their phases. Diffraction data that are reliably phased will add constructively, whereas data with phases that are inconsistent over many iterates will add randomly, leading to reduced intensity in the reconstruction compared to the recorded intensities I_data. The ratio I_recon/I_data is shown alongside the theoretical modulation transfer function (MTF) of conventional imaging optics with an efficiency of 75% and Rayleigh resolutions of 30 and 15 nm, respectively.

Fig. 3.

Images of a freeze-dried yeast cell. A was obtained by phasing the diffraction data in Fig. 1, whereas C and D were obtained from reconstructions of two separate, slightly lower exposure data sets acquired with the cell tilted by 3° (C) and 4° (D) relative to A (Movie 2, which is published as supporting information on the PNAS web site, displays reconstructed images at 1° intervals over a 7° range). Insets in C and D show ≈30-nm fine features at the cell and nuclear membrane regions that are reproduced consistently in these separate recordings and reconstructions, even though these 2D reconstructions are projections along the beam axis with some blurring as a result of defocus. The renderings of the complex-valued reconstructions use brightness to represent magnitude and hue to represent phase (the color scale indicates reconstructed phase values). A is labeled according to a provisional identification of the nucleus (N), a storage vacuole (V), and the cell membrane (M). B shows a National Synchrotron Light Source X1A2 STXM (27) image taken of the same cell using 540-eV x-rays and a zone plate with an estimated Rayleigh resolution of 42 nm; this image shows absorption effects only, so it is shown in grayscale. The STXM image is shown here for comparison purposes only; it was taken at a different photon energy and in a different contrast mode (incoherent brightfield) than applies to the reconstructed diffraction data. The information contained in the STXM image was not used in any way in obtaining the diffraction reconstruction.